In-silico modelling of tumour-immune system interactions for glioblastomas

In the present work, a new mathematical approach for modelling the influence of the immune system, more precisely of microglial cells, on the progression of malignant primary brain tumours is presented. A hybrid approach is used to model the cellular tumour progression, the development of the local nutrient concentration and of the density of the extracellular matrix (ECM). The resting microglia in primary brain tumours are activated and attracted by signals emitted by tumour cells, which are described by a partial differential equation. The secretion of matrix degrading enzymes from amoeboid immune cells can be modelled with the help of an additional term for the degradation of the ECM. This supports a more invasive migration of tumour cells. To our knowledge, we present for the first time a model of microglial cells in the context of tumour growth. The qualitative results are identical to the cell arrangements described in the literature. In addition, the comparison with in-vitro data matches in a qualitative manner. The proposed model, thus, represents a promising approach for modelling brain tumour growth at the cellular level in the light of the innate immune system.